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NumericalAlgebraicGeometry :: randomInitialPair

randomInitialPair -- a random initial pair

Synopsis

Description

Generates a start system S that has an equal chance of reaching any of the solutions of the target system T. For more details see: C. Beltran and A. Leykin, "Certified numerical homotopy tracking", arXiv:0911.1783

i1 : T = randomSd {2,3};
i2 : (S,solsS) = randomInitialPair T

                                2                                            
o2 = ({(- .108408 - .32079*ii)x1  + (.0250007 + .0330164*ii)x1*x2 + (.0767552
     ------------------------------------------------------------------------
                    2                                               
     - .265559*ii)x2  + (- .368326 - .611296*ii)x1*x3 + (- .118685 +
     ------------------------------------------------------------------------
                                                 2               
     .13041*ii)x2*x3 + (- .082634 + .277987*ii)x3 , (- .0583529 +
     ------------------------------------------------------------------------
                   3                           2                
     .0341006*ii)x1  + (.333722 + .159158*ii)x1 x2 + (.0880181 +
     ------------------------------------------------------------------------
                     2                              3             
     .131936*ii)x1*x2  + (- .112355 + .0583659*ii)x2  + (.582957 +
     ------------------------------------------------------------------------
                 2                                                      
     .11855*ii)x1 x3 + (- .00322147 - .844068*ii)x1*x2*x3 + (- .146446 -
     ------------------------------------------------------------------------
                  2                                  2               
     .222541*ii)x2 x3 + (- .208228 + .183028*ii)x1*x3  + (- .319908 +
     ------------------------------------------------------------------------
                      2                         3
     .0225572*ii)x2*x3  + (.238863 + .2494*ii)x3 }, {{.314832+.404481*ii,
     ------------------------------------------------------------------------
     .398164-.637397*ii, .382106+.162669*ii}})

o2 : Sequence
i3 : M = track(S,T,solsS,gamma=>0.6+0.8*ii,Software=>M2)

o3 = {{.741955+.116903*ii, .258269-.303162*ii, .336708+.404789*ii}}

o3 : List

See also

Ways to use randomInitialPair :